Simultaneous estimation of the masses of Mars, Phobos, and Deimos using spacecraft distant encounters

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Abstract
The masses of Mars and its satellites, Phobos and Deimos, have been estimated from the Mariner 9 and Viking 1 and 2 Orbiter tracking data. These spacecraft were sensitive to the gravitational force of Mars as well as to its satellites. Although the satellite masses are eight orders of magnitude smaller than Mars, their regular effect on the orbits of the spacecraft is evident in the tracking data and has enabled us to derive their masses simultaneously with that of Mars. Our method for estimating the satellite masses uses the many “distant encounters” of the spacecraft with these small bodies rather than the few “close encounters” used in previous studies. The mass estimate for Phobos leads to a mean density of 1530±100 kg m−3 based on a volume of 5748±190 km³ (Thomas, 1993), while the mass estimate of Deimos leads to a poorly constrained mean density of 1340±828 kg m−3 based on a volume of 1017±130 km³ (Thomas, 1993). Our analysis confirms, within the bounds of error, the anomalously low density of Phobos using an independent method and data set. If the result is valid within several times the estimated error (1σ), then factors other than composition, i.e., porosity, a thick regolith and/or a significant interior ice content, are required to explain the observed mass of this body.